As has been said many, many times before, most schools do not have unlimited funds for FA and do make all of their decisions based on need. A few schools have enough money to do whatever the heck they want. But those schools are the most competitive in every other way, too.
The fact that some schools will offer insanely generous FA deals far and above what you might get at another school should be all the proof anyone needs to see that the FA thing is as much of a subjective contest as the admission process.
But that’s what you signed up for if you need FA and want to give these sorts of schools a try.